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strojnjashka [21]
3 years ago
13

What is the derivative of Y =x√(2x + 1)/e^xsin^3(x).?

Mathematics
1 answer:
blagie [28]3 years ago
3 0
-\dfrac{\mathrm{e}^{-x}\left(\left(2x^2-2x-1\right)\sin\left(x\right)+\left(6x^2+3x\right)\cos\left(x\right)\right)}{\sqrt{2x+1}\sin^4\left(x\right)}.
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❊ Simplify :
Nataliya [291]
<h3>Need to Do :- </h3>
  • To simplify the given expression .

\red{\frak{Given}}\Bigg\{ \sf \dfrac{x - 1}{ {x}^{2} - 3x + 2} + \dfrac{x - 2}{ {x}^{2} - 5x + 6 } + \dfrac{x - 5}{ {x}^{2} - 8x + 15 }

\rule{200}4

\sf\longrightarrow \small  \dfrac{x - 1}{ {x}^{2} - 3x + 2} + \dfrac{x - 2}{ {x}^{2} - 5x + 6 } + \dfrac{x - 5}{ {x}^{2} - 8x + 15 } \\\\\\\sf\longrightarrow \small  \dfrac{ x-1}{x^2-x -2x +2} +\dfrac{ x-2}{x^2-3x-2x+6} +\dfrac{ x -5}{x^2-5x -3x + 15 } \\\\\\\sf\longrightarrow\small \dfrac{ x -1}{ x ( x - 1) -2(x-1) } +\dfrac{ x-2}{x ( x -3) -2( x -3)} +\dfrac{ x -5}{ x(x-5) -3( x -5) }  \\\\\\\sf\longrightarrow \small \dfrac{ x -1}{ ( x-2) (x-1) } +\dfrac{ x-2}{( x -2)(x-3) } +\dfrac{ x -5}{ (x-3)(x-5)  } \\\\\\\sf\longrightarrow\small \dfrac{ 1}{ x-2} +\dfrac{ 1}{ x -3} +\dfrac{1}{ x -3}   \\\\\\\sf\longrightarrow   \small  \dfrac{1}{x-2} +\dfrac{2}{x-3}  \\\\\\\sf\longrightarrow   \small \dfrac{ x-3 +2(x-2)}{ ( x -3)(x-2) }  \\\\\\\sf\longrightarrow   \small \dfrac{ x - 3 +2x -4 }{ (x-3)(x-2) }     \\\\\\\sf\longrightarrow   \underset{\blue{\sf Required \ Answer  }}{\underbrace{\boxed{\pink{\frak{  \dfrac{ 3x -7}{ ( x -2)(x-3) } }}}}}

\rule{200}4

5 0
2 years ago
Read 2 more answers
Please show your work<br> What is the solution of the equation <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B2x%2B13%7D%20-5%3D
Hatshy [7]
Add the five to each side.
then square it to get rid of the square root
2x+13=(5+x)^2
2x+13=x^2+10x+25
2x=x^2+10x+12
x^2+8x+12=0
(x+6)(x+2)
x+6=0
x+2=0
answers are -2 and -6, however, when pluging -6 in it doesnt work, so it is only -2.
3 0
3 years ago
suppose a weather app says that the probability of rain today is 30%. What is the complement of the event ""rain today"" what is
ValentinkaMS [17]

Answer:

The complement event would be: "No rain today"

Its probability would be 70%

Step-by-step explanation:

Given the event:

A= rain today

The probability of rain today is 30%

P(A)=30%=0.3

The complement event has all the values that are not included in the event.

The complement event would be:

A'= No rain today

The probability of a event is the subtraction between 1 and the complement event:

P(A')=1-P(A)

Then, the probability of the event "No rain today" will be:

P(A')=1-0.3=0.7=70%

4 0
3 years ago
Carly and janiya put some money into their money boxes every week. the amounts of money (y), in dollars, in their money boxes af
Lelu [443]
Carly : y = 60x + 40
janiya : y = 50x + 80

60x + 40 = 50x + 80
60x - 50x = 80 - 40
10x = 40
x = 40/10
x = 4 <=== so at 4 weeks, they will have the same amount of money <==
The money they have is : y = 60(4) + 40.....y = $ 280 <=

so ur answer is : 4 weeks, $ 280
8 0
3 years ago
Please Help ASAP!! NEED DONE QUICKLY!!
Kipish [7]

Answer:

z=t and y = 4y -- 6 for any t?

5 0
2 years ago
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